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Cooperativity and modularity in protein folding

A simple statistical mechanical model proposed by Wako and Sait$\hat{\rm o}$ has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Mu$\tilde{\rm n}$oz and Eaton and has since been referred to as the Wako-Sait$\hat{\rm o}$-Mu$\tilde{\rm n}$oz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Sait$\hat{\rm o}$ emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The $ϕ$-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.